Khan Academy Static

Proofs_for_the_derivatives_of_e_and_ln_x_

The derivatives of eˣ and ln(x) may be simple, but proving them is a different story. Learn all about it here.

Review_Advanced_differentiation

Review your knowledge of the advanced differentiation topics with some challenge problems.

Implicit_differentiation_introduction

Some two-variable relationships cannot be turned into a function, like the circle equation x²+y²=4. Implicit differentiation allows us to find the derivative of y with respect to x, even in such equations.

Logarithmic_differentiation

In logarithmic differentiation, we find the derivative of the natural log of a function instead of the derivative of the function itself. It may surprise you, but this can sometimes actually be easier than regular differentiation, if not the only available option. For example, finding the derivative of xˣ.

Implicit_differentiation_advanced_examples_

Tackle some more advanced problems of implicit differentiation. For example, find dy/dx for e^(xy²)=x-y.

Inverse_trig_functions_differentiation

Implicit differentiation allows us to find the derivatives of arcsin(x), arccos(x), and arctan(x).

Derivatives_of_inverse_functions

Implicit differentiation provides us with the relationship between the derivatives of inverse functions: if f and g are inverse functions, then f’(x)=1/(g’(f(x)). Get comfortable working with this relationship.

Disguised_derivatives

Equipped with knowledge about the derivatives of all common functions, evaluate some limits that represent various derivatives.

Higher_order_derivatives

The derivative is a function, and as such it has its own derivative! The same goes for the derivative of the derivative, and so forth. These are all called higher-order derivatives.